Simplify the following expression: $ k = \dfrac{p + 5}{3p - 10} + \dfrac{-10}{7} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{p + 5}{3p - 10} \times \dfrac{7}{7} = \dfrac{7p + 35}{21p - 70} $ Multiply the second expression by $\dfrac{3p - 10}{3p - 10}$ $ \dfrac{-10}{7} \times \dfrac{3p - 10}{3p - 10} = \dfrac{-30p + 100}{21p - 70} $ Therefore $ k = \dfrac{7p + 35}{21p - 70} + \dfrac{-30p + 100}{21p - 70} $ Now the expressions have the same denominator we can simply add the numerators: $k = \dfrac{7p + 35 - 30p + 100}{21p - 70} $ $k = \dfrac{-23p + 135}{21p - 70}$